A163662 A020988 written in base 2.

10, 1010, 101010, 10101010, 1010101010, 101010101010, 10101010101010, 1010101010101010, 101010101010101010, 10101010101010101010, 1010101010101010101010, 101010101010101010101010, 10101010101010101010101010, 1010101010101010101010101010, 101010101010101010101010101010

Offset: 1

Author

Jaroslav Krizek, Aug 02 2009

Keywords

• nonn
• base
• easy

Comments

The digits are n concatenated blocks of (10).

Smallest number having alternating bit sum -n. Cf. A065359. - Washington Bomfim, Jan 22 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 1..495
• Index entries for linear recurrences with constant coefficients, signature (101,-100).

Crossrefs

Cf. A065359, A094028.

Programs

Maple

A163662 := proc(n) add(10^(2*k-1),k=1..n) ; end: seq(A163662(n),n=1..30) ; # R. J. Mathar, Jul 08 2009

Mathematica

Table[(10/99)*(10^(2*n) - 1), {n,1,50}] (* G. C. Greubel, Aug 01 2017 *)
Table[FromDigits[PadRight[{},2n,{1,0}]],{n,20}] (* or *) LinearRecurrence[ {101,-100},{10,1010},20] (* Harvey P. Dale, Jan 08 2020 *)

PARI

x='x+O('x^50); Vec(10*x/((100*x-1)*(x-1))) \\ G. C. Greubel, Aug 01 2017

Formula

a(n) = Sum_{k=1..n} 10^(2*k-1).

From R. J. Mathar, Jul 08 2009: (Start)

a(n) = 100*a(n-1) + 10.

a(n) = 101*a(n-1) - 100*a(n-2).

G.f.: 10*x/((100*x-1)*(x-1)). (End)

From G. C. Greubel, Aug 01 2017: (Start)

a(n) = (10/99)*(10^(2*n) - 1).

E.g.f.: (10/99)*(exp(100*x) - exp(x)). (End)

a(n) = 10*A094028(n-1). - Elmo R. Oliveira, Jul 23 2025